分析汇率波动：针对GBP/USD和EUR/GBP货币对的GARCH、EWMA和IV模型比较研究
Analyzing Currency Fluctuations: A Comparative Study of GARCH, EWMA, and IV Models for GBP/USD and EUR/GBP Pairs
AI总结：
本研究比较了GARCH、EWMA和IV模型在预测GBP/USD和EUR/GBP货币对20天波动率方面的表现，发现GARCH模型结合滚动窗口适用于前者，而结合隐含波动率的GARCH与OLS模型更适用于后者。
摘要：
在本研究中，我们考察了英镑（GBP）价值的波动。我们特别关注其与美元（USD）和欧元（EUR）货币对之间的关系。利用2018年6月15日至2023年6月15日的数据，我们应用各种数学模型来评估它们在预测这些货币对日收益率20天变化方面的有效性。我们的分析涉及实现指数加权移动平均（EWMA）、广义自回归条件异方差（GARCH）模型和隐含波动率（IV）模型。为了评估它们的性能，我们使用均方根误差（RMSE）和平均绝对误差（MAE）指标比较了它们预测的准确性。我们深入探讨了GARCH模型的复杂性，检验了其在应用于所提供数据集时的统计特征。我们的研究结果表明，在EUR/GBP货币对中存在不对称收益，而对于GBP/USD货币对，此类证据尚无定论。此外，我们观察到，当假设残差服从标准t分布而非标准正态分布时，GARCH类模型能更好地拟合数据。进一步地，我们研究了GARCH类模型中不同预测技术的有效性。通过比较滚动窗口预测与扩展窗口预测，我们发现在测试场景中两种方法均无绝对的优越性。我们的实验表明，对于GBP/USD货币对，最准确的波动率预测来自于采用滚动窗口方法的GARCH模型。相反，对于EUR/GBP货币对，最佳预测来自于GARCH模型和将汇率年化隐含波动率作为自变量的普通最小二乘法（OLS）模型。
英文摘要：
In this study, we examine the fluctuation in the value of the Great Britain Pound (GBP). We focus particularly on its relationship with the United States Dollar (USD) and the Euro (EUR) currency pairs. Utilizing data from June 15, 2018, to June 15, 2023, we apply various mathematical models to assess their effectiveness in predicting the 20-day variation in the pairs' daily returns. Our analysis involves the implementation of Exponentially Weighted Moving Average (EWMA), Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and Implied Volatility (IV) models. To evaluate their performance, we compare the accuracy of their predictions using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) metrics. We delve into the intricacies of GARCH models, examining their statistical characteristics when applied to the provided dataset. Our findings suggest the existence of asymmetric returns in the EUR/GBP pair, while such evidence is inconclusive for the GBP/USD pair. Additionally, we observe that GARCH-type models better fit the data when assuming residuals follow a standard t-distribution rather than a standard normal distribution. Furthermore, we investigate the efficacy of different forecasting techniques within GARCH-type models. Comparing rolling window forecasts to expanding window forecasts, we find no definitive superiority in either approach across the tested scenarios. Our experiments reveal that for the GBP/USD pair, the most accurate volatility forecasts stem from the utilization of GARCH models employing a rolling window methodology. Conversely, for the EUR/GBP pair, optimal forecasts are derived from GARCH models and Ordinary Least Squares (OLS) models incorporating the annualized implied volatility of the exchange rate as an independent variable.
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